2 Answers
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To answer your first question, we should not simply accept Sinaiticus as the source of the truth for the New Testament. It has great weight in debates from its age, but age is not the final arbiter in textual considerations.

Codex Sinaiticus was made in the 4th century on parchment using capital letters (a manuscript in all capitals is called an "uncial"). It was discovered in the 19th century, surpassing Vaticanus as the most complete manuscript. Codex Sinaiticus is considered by most textual scholars of the New Testament to be the best complete manuscript. It and Vaticanus are hypothesized to be part of Emperor Constantine's project, though this has never been conclusively proven either way.

It should be understood that "complete manuscript" when used by a textual critic does not necessarily mean 100% of it has survived. "Complete" is a technical term meaning that the manuscript has the beginning and end of the book in question. For example, a "complete copy of John" would be required to have John 1:1 and John 21:25 and substantial portions of those verses between.

Originally, Sinaiticus had the entire, Greek Old Testament (the Septuagint) as well as the complete New Testament. Only half of the Old Testament has survived, but the New Testament is complete in that all books are represented while only a few passages and verses are missing due to pages missing, holes in the pages, or scribal exclusions.

While it is significant that Sinaiticus is the oldest complete manuscript, it is not the oldest manuscript. There are pieces of different books that are much older. P52 (a piece of John's Gospel) has been dated to AD 117 at the oldest based on the style of hand writing (though some argue for a date into the second half of the first century). Possibly even older, is a recently discovered fragment of Mark that some are saying they are "certain" it is from the first century. There are also copies of entire books that are older than Sinaiticus. For example, P46 contains all of Hebrews, Ephesians, Philippians, Galatians, and Colossians, and virtually all of 1 and 2 Corinthians. It is dated between AD 175 and 225. Likeiwse, P66 (from roughly the same time period) contains most of John, but the ending is missing so it is not considered complete.

For the Gospels, Sinaiticus is generally considered among scholars as the second most reliable witness of the text (after Vaticanus); in the Acts of the Apostles, its text is equal to that of Vaticanus; in the Epistles, Sinaiticus is the most reliable witness of the text. In the Book of Revelation, however, its text is corrupted and is considered of poor quality, and inferior to the texts of Codex Alexandrinus, Papyrus 47, and even some minuscule manuscripts in this place (for example, Minuscule 2053, 2062).

However, even in the epistles, where it is considered the most reliable, it is not merely accepted. Textual critics and scholars will compare many manuscripts to determine the original text. By studying the copies and copying styles, they have put together a list of errors that scribes were likely to make and they can compare manuscripts to see which wording is more likely to be original.

Although Frank has a great answer above, I thought I'd add a couple of things. The question of the proximity of a text to the original depends on a number of factors, age being an important one, but certainly not the only one.

To think about this, it is necessary to think about the process of manuscript manufacture in the early years of the church. Manuscripts were copied meticulously by hand, but like all manual processes they suffered from copying errors. There are basically two types of errors, deliberate copying errors where the copyist chose to write something that was not in his exemplar, and accidental copying errors where the copyist accidentally wrote something different than the exemplar.

Age is actually more a proxy for generational number -- the original was first generation, the copy was the second generation, the copy of the copy the third and so forth. Consequently, since the age of the manuscript approximates the number of times it has been copied, it approximates the generational number, and with each generation there is the possibility of the introduction of errors.

So the value of a manuscript is both dependent on the generational number, and the quality of the copying at each generation.

The age and consequently generational number is determined via a science called paleography, where the style of handwriting and the materials used are used to estimate both its age and its geographical origin. The ingenuity of the people who do this is quite remarkable. I'd definitely recommend learning more about it just to be amazed at what they do.

The two different error modes tend to be determined in two different ways.

Accidental errors are usually categorized into typical and common errors. For example, copying text from a preceding line, or skipping a line, or substituting one word with a similar spelling for another, or substituting Jesus words from one gospel into another.
The quality of a manuscript can be pretty readily judged by looking at non consequential errors -- how many unimportant errors did the scribe make as a measure of how many consequential errors did they make.

In terms of deliberate errors, where the scribe "corrected" the text, we are in more trouble. However, this is determined by looking at many different manuscripts, comparing them based on various criteria, and identifying where they are significantly different from the "mainstream."

However, majoritarianism does not win here. For example the majority of Greek texts are classified as Byzantine. Most early English translations came from the critical version of this called Textus Receptus. However, it is not widely regarded as a good reflection or the original because of the two modes of error mentioned above.

So the answer to the question is simply that Sinacticus is a pretty faithful rendition of the original, but Nestle and Aland is better. Nonehtheless, as I have said here before, everyone who can read Greek absolutely should get his head out of the clean, sanitized version in N&A and look at some of the early texts, such as the beautiful Sinacticus, or Chester Beaty papyruses. It will give yo ua whole new perspective.

BTW, I did not even address the question of what does "original Greek New Testament" mean. Questions like the originality of John 21, for example, are far from trivial.

@Mawia: I just mean that according to most scholars, the author of Matthew used a written copy of Mark as the source for about half of the material of his gospel. (According to a minority of scholars, the copying goes the other way.) Thus the "original" of half of the material in Matthew is Mark. I mentioned this example, because it's less controversial than say John 21 or Luke 1-2 being later additions to previously existing works. At any rate, this is getting very far afield from the original question.
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NoahFeb 6 '13 at 5:35

@NoahSnyder My faith convince me that all 4 Gospels were written in isolation from each other.
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MawiaFeb 6 '13 at 5:40

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In particular, I'd be very surprised to find conservative scholars who think Luke was written in isolation from the other gospels, in light of Luke 1:1-3.
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NoahFeb 6 '13 at 17:11